The Reynold's Stress Models (RSM), also known as the Reynold's Stress Transport (RST) models, are higher level, elaborate turbulence models. The method of closure employedis usually called a ''Second Order Closure''. This modelling approach originates from the work by [[#References|[Launder (1975)]]]. In RSM, the eddy viscosity approach has been discarded and the Reynolds stresses are directly computed. The exact Reynolds stress transport equation accounts for the directional effects of the Reynolds stress fields.

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The Reynold's Stress Models (RSM), also known as the Reynold's Stress Transport (RST) models, are higher level, elaborate turbulence models. The method of closure employed is usually called a ''Second Order Closure''. This modelling approach originates from the work by [[#References|[Launder (1975)]]]. In RSM, the eddy viscosity approach has been discarded and the Reynolds stresses are directly computed. The exact Reynolds stress transport equation accounts for the directional effects of the Reynolds stress fields.

Introduction

The Reynold's Stress Models (RSM), also known as the Reynold's Stress Transport (RST) models, are higher level, elaborate turbulence models. The method of closure employed is usually called a Second Order Closure. This modelling approach originates from the work by [Launder (1975)]. In RSM, the eddy viscosity approach has been discarded and the Reynolds stresses are directly computed. The exact Reynolds stress transport equation accounts for the directional effects of the Reynolds stress fields.

Equations

The Reynolds stress model involves calculation of the individual Reynolds stresses, , using differential transport equations. The individual Reynolds stresses are then used to obtain closure of the Reynolds-averaged momentum equation.

The exact transport equations for the transport of the Reynolds stresses, , may be written as follows:

Of these terms, , , , and do not require modeling. After all, , , , and have to be modeled for closing the equations.

Modeling Turbulent Diffusive Transport

Modeling the Pressure-Strain Term

Effects of Buoyancy on Turbulence

Modeling the Turbulence Kinetic Energy

Modeling the Dissipation Rate

Modeling the Turbulent Viscosity

Boundary Conditions for the Reynolds Stresses

Convective Heat and Mass Transfer Modeling

Return-to-isotropy models

For an anisotropic turbulence, the Reynolds stress tensor,
, is usually anisotropic. The
second and third invariances of the Reynolds-stress anisotropic
tensor are nontrivial, where
and
. It is naturally to suppose
that the anisotropy of the Reynolds-stress tensor results from the
anisotropy of turbulent production, dissipation, transport,
pressure-stain-rate, and the viscous diffusive tensors. The
Reynolds-stress tensor returns to isotropy when the anisotropy of
these turbulent components return to isotropy. Such a correlation is
described by the Reynolds stress transport equation. Based on these
consideration, a number of turbulent models, such as Rotta's model
and Lumley's return-to-isotropy model, have been established.

Rotta's model describes the linear return-to-isotropy behavior of a
low Reynolds number homogenous turbulence in which the turbulent
production, transport, and rapid pressure-strain-rate are
negligible. The turbulence dissipation and slow pressure-strain-rate